Abstract

We investigate the lattice QCD Dirac operator with staggered fermions at temperatures around the chiral phase transition. We present evidence of a metal-insulator transition in the low lying modes of the Dirac operator around the same temperature as the chiral phase transition. This strongly suggests the phenomenon of Anderson localization drives the QCD vacuum to the chirally symmetric phase in a way similar to a metal-insulator transition in a disordered conductor. We also discuss how Anderson localization affects the usual phenomenological treatment of phase transitions a la Ginzburg-Landau.

Lattice QCD with four flavors of light dynamical quarks is simulated on a 10/sup 3/ x 6 lattice in order to study the finite-temperature transition in the chiral limit. The mass used, m = 0.025 (in lattice units), is half the smallest value previously used on this size lattice. We find evidence for a finite-temperature phase transition which is absent for intermediate masses. The time evolution of the system shows both long correlation times characteristic of a nearby critical point and abrupt changes.

We have simulated lattice QCD directly in the chiral limit of zero quark mass by adding an additional, irrelevant 4-fermion interaction to the standard action. Using lattices having temporal extent of six and spatial extents of twelve and eighteen, we find that the theory with 2 massless staggered quark flavors has a second-order finite-temperature phase transition. The critical exponents {beta}{sub mag}, {delta} and {nu} are measured and favour tricritical behaviour over that expected by universality arguments. The pion screening mass is consistent with zero below the transition, but is degenerate with the nonzero {sigma}(f{sub 0}) mass above the transition, indicatingmore » the restoration of chiral symmetry.« less

A previous finite-size study for the chiral phase transition of two-flavor QCD is extended to a smaller quark mass of {ital m}{sub {ital q}}=0.0125 in lattice units. The characteristics of the system for lattice sizes (6{sup 3}--12{sup 3}){times}4 are found to be quite similar to those for {ital m}{sub {ital q}}=0.025. The increase of susceptibilities over this range of the spatial size is still too mild to discriminate among the order of the transition also at this small quark mass.

A finite-size test was carried out for the finite-temperature chiral phase transition in QCD for flavor number {ital N}{sub {ital f}}=4 and 2 on a lattice with four time slices using the Kogut-Susskind quark action at quark mass of 0.025 in lattice units. All the evidence supports a first-order transition for {ital N}{sub {ital f}}=4. For {ital N}{sub {ital f}}=2, however, the data on spatial lattice up to 12{sup 3} fail to yield convincing finite-size signatures for a first-order transition at this quark mass.

Understanding the nature of the chiral phase transition in two-flavor QCD has proven to be a challenging task. The prediction of a second-order transition with critical behavior in the universality class of the O(4) spin model is not verified for staggered fermions of small masses, although it can be shown (by an unambiguous normalization of the data) that better scaling is obtained for the existing data at larger (unphysical) masses. Here we present data obtained at an even larger value of the quark mass, showing good scaling for the first time. We argue that the deviations from O(4) scaling atmore » smaller masses may come from systematic errors in the simulation.« less